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Results tagged with variance
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user 35658
Used for questions related to statistical measure "variance", i.e. a second central moment of a random variable. The variance is a risk measure.
5
votes
Accepted
Market-maker's gain variance
So, the expectation of the of jump amount, MM,
$ = E(MM) = \frac{\phi}{2} \times J + \frac{\phi}{2} \times -J + (1-\phi) \times 0 = 0$
The variance, $\sigma^2_{MM}$ of the jump amount = $E( MM - 0)^2 …
- 1,178
1
vote
T-statistics on monthly returns vs annualized monthly returns
The background is that you have an average monthly return $\bar{r}_{m} = \frac{1}{12}\sum_{i=1}^{12} r_{i}$ and a monthly variance estimate $\sigma^2_{\bar{r}_{m}}$ where $\sigma^2_{\bar{r}_{m}} = \frac … Now, we want to convert from monthly to yearly ( we assume that the returns can be added because they are small enough ) to get the yearly return and yearly variance, so we need to make the assumption …
- 1,178
1
vote
ARMA moments proof
- \beta L)} $
Since $|\beta| < 1.0 $, this is an infinite sum that converges:
$X_t = \sum_{i=0}^\infty \beta^{i}( 1 + \theta L) u_{t-i}$
The $u_{t}$ are independent and normal with mean zero and variance … $\sigma^2$ so you have a converging infinite sum of iid random variables so you should be able to calculate the mean and the variance. …
- 1,178